CN110389527B - Heterogeneous estimation-based MEMS gyroscope sliding mode control method - Google Patents

Heterogeneous estimation-based MEMS gyroscope sliding mode control method Download PDF

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CN110389527B
CN110389527B CN201910648290.3A CN201910648290A CN110389527B CN 110389527 B CN110389527 B CN 110389527B CN 201910648290 A CN201910648290 A CN 201910648290A CN 110389527 B CN110389527 B CN 110389527B
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许斌
张睿
张鹏超
杨婷
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Northwestern Polytechnical University
Shaanxi University of Technology
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Shaanxi University of Technology
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Abstract

The invention relates to a heterogeneous estimation-based sliding-mode control method for an MEMS gyroscope, and belongs to the field of intelligent instruments. The method converts a gyroscope kinetic model into a dimensionless kinetic linear parameterized model; the current data and the historical data are combined to jointly design a parameter self-adaption law to be identified, so that parameter identification is realized; designing a self-adaptive neural network to adjust the weight of the neural network on line, and realizing effective estimation on uncertainty; the sliding mode controller is designed to realize the drive control of the MEMS gyroscope, and meanwhile, the robustness of the system to external interference is improved. The MEMS gyroscope sliding mode control method based on historical data learning and parameter identification based on heterogeneous estimation can solve the problem that the control precision of a driving control system is limited, realize high-precision gyroscope driving control, identify dynamic parameters and further improve the performance of the MEMS gyroscope.

Description

Heterogeneous estimation-based MEMS gyroscope sliding mode control method
Technical Field
The invention relates to a drive control method of an MEMS gyroscope, in particular to an MEMS gyroscope sliding mode control method based on heterogeneous estimation, and belongs to the field of intelligent instruments.
Background
In practical engineering application, changes of working environments such as temperature, air pressure, magnetic field and vibration of the MEMS gyroscope pose challenges for gyro drive control, and particularly, a controller lacking adaptive capacity is difficult to adapt to a dynamically changing environment. Two commonly used solutions are: (1) the hardware design is improved, and the influence of shielding the external environment by the isolation component is increased; (2) the design scheme of the controller is improved, and the self-adaptive capacity of the controller is enhanced.
Because Sliding Mode Control is insensitive to external environment change and the system robustness is strong, an MEMS Gyroscope Global Sliding Mode Control method based on an RBF Neural Network is provided in the text of Adaptive Global Sliding Mode Control for MEMS Gyroscope Using RBF Neural Network (Yundi Chu and Juntao Fei, physical schemes in Engineering, 2015), the Neural Network is adopted to adjust Sliding Mode switching gain, and a dynamic model parameter identification result is provided at the same time. However, this method mainly focuses on the problem of sliding mode buffeting, and it is difficult to ensure the driving control accuracy.
Disclosure of Invention
Technical problem to be solved
In order to solve the problem that the control precision of a driving control system in the prior art is limited, the invention provides an MEMS gyroscope sliding mode control method based on heterogeneous estimation. The method combines the current data and the historical data to jointly construct a parameter self-adaptive law to be identified, and realizes parameter identification; designing a self-adaptive neural network to adjust the weight of the neural network on line, and realizing effective estimation on uncertainty; the sliding mode controller is designed to realize the drive control of the MEMS gyroscope, and meanwhile, the robustness of the system to external interference is improved.
Technical scheme
A sliding mode control method of an MEMS gyroscope based on heterogeneous estimation is characterized by comprising the following steps:
step 1: the MEMS gyroscopic dynamics model considering the presence of quadrature errors and system uncertainty is:
Figure BDA0002134299120000021
where m is the mass of the proof mass, ΩzIn order to input the angular velocity for the gyro,
Figure BDA0002134299120000022
and x is the acceleration, velocity and displacement of the MEMS gyroscope proof mass along the driving shaft respectively,
Figure BDA0002134299120000023
and y are acceleration, velocity and displacement along the detection axis respectively,
Figure BDA0002134299120000024
and
Figure BDA0002134299120000025
as an electrostatic driving force, cxxAnd cyyAs damping coefficient, kxxAnd kyyIn order to be a stiffness factor, the stiffness factor,
Figure BDA0002134299120000026
and
Figure BDA0002134299120000027
is a nonlinear coefficient, cxyAnd cyxTo damp the coupling coefficient, kxyAnd kyxIs the stiffness coupling coefficient; and is
Figure BDA0002134299120000028
Figure BDA0002134299120000029
Wherein
Figure BDA00021342991200000210
And
Figure BDA00021342991200000211
is a parameter nominal value, is selected according to a certain model of vibrating silicon micromechanical gyroscope, and is delta kxx、Δkyy、Δcxx、Δcyy、
Figure BDA00021342991200000212
Δkxy、Δkyx、ΔcxyAnd Δ cyxIs an unknown uncertain parameter;
taking the dimensionless time t as omegaot*Non-dimensionalized displacement x ═ x*/q0，y＝y*/q0Wherein ω is0As reference frequency, q0For reference length, the MEMS gyroscopic dynamics model is dimensionless and divided by the equation on both sides simultaneously
Figure BDA00021342991200000213
To obtain
Figure BDA00021342991200000214
Wherein the content of the first and second substances,
Figure BDA00021342991200000215
and x is the dimensionless acceleration, the dimensionless speed and the dimensionless displacement of the MEMS gyroscope proof mass along the driving shaft respectively,
Figure BDA00021342991200000216
and y is the dimensionless acceleration, the dimensionless speed and the dimensionless displacement along the detection axis, respectively;
redefining
Figure BDA0002134299120000031
Figure BDA0002134299120000032
Figure BDA0002134299120000033
Figure BDA00021342991200000316
Figure BDA0002134299120000034
Figure BDA0002134299120000035
Figure BDA0002134299120000036
Figure BDA0002134299120000037
Figure BDA0002134299120000038
Figure BDA0002134299120000039
The formula (2) can be represented as
Figure BDA00021342991200000310
Definition of θ ═ x, y]T，F＝[f1,f2]T，ΔF＝[Δf1,Δf2]T，U＝[u1,u2]TThen formula (3) can be written as
Figure BDA00021342991200000311
Suppose that
Figure BDA00021342991200000312
Is the unknown parameter matrix to be identified,
Figure BDA00021342991200000313
if the vector is a continuous micro regression function vector, performing linear parameterization on the F to obtain
F＝WΦ (5)
Wherein the content of the first and second substances,
Figure BDA00021342991200000314
Figure BDA00021342991200000315
constructing neural networks
Figure BDA0002134299120000041
Approaches Δ F to obtain
Figure BDA0002134299120000042
Wherein the content of the first and second substances,
Figure BDA0002134299120000043
is the input vector of the neural network and,
Figure BDA0002134299120000044
is the weight matrix of the neural network, M is the number of nodes of the neural network,
Figure BDA0002134299120000045
is a base vector, the q (q is 1,2, …, M) th element of which is defined as the following Gaussian function
Figure BDA0002134299120000046
Wherein σqIs the standard deviation of the gaussian to be designed,
Figure BDA0002134299120000047
is the center of the gaussian function to be designed;
step 2: the reference trajectory given for MEMS gyroscopic dynamics (1) is
Figure BDA0002134299120000048
Wherein the content of the first and second substances,
Figure BDA0002134299120000049
and
Figure BDA00021342991200000410
respectively reference vibration displacement signals of the proof mass along the drive axis and the detection axis,
Figure BDA00021342991200000411
and
Figure BDA00021342991200000412
reference amplitudes, ω, of drive and sense shaft vibrations, respectively1And ω2Respectively the reference angular frequencies of the drive shaft and the detection shaft vibrations,
Figure BDA00021342991200000413
and
Figure BDA00021342991200000414
the phases of the drive shaft and the detection shaft vibration respectively;
the reference trajectory of the dimensionless kinetic equation (4) is
θd＝[xd,yd]T (9)
Wherein the content of the first and second substances,
Figure BDA00021342991200000415
and the parameters to be designed
Figure BDA00021342991200000416
Figure BDA00021342991200000417
Defining a tracking error as
e＝θ-θd (10)
The slip form surface is designed as
Figure BDA00021342991200000418
Wherein the content of the first and second substances,
Figure BDA00021342991200000419
a matrix satisfying the Hurwitz condition;
the controller is designed as
U＝Un+Us+Ul (12)
Figure BDA0002134299120000051
Us＝-Kss(14)
Figure BDA0002134299120000052
Wherein the parameter to be designed
Figure BDA0002134299120000053
The Hurwitz condition is met,
Figure BDA0002134299120000054
is an estimate of W;
defining a prediction error as
Figure BDA0002134299120000055
Wherein the content of the first and second substances,
Figure BDA0002134299120000056
τdis a normal number to be designed;
giving an adaptation law of the parameters
Figure BDA0002134299120000057
Wherein, the first term on the right side of the equation is calculated by using the data at the current moment, and the second term is calculated by using tau epsilon [ t-tau ]d,t]Historical data calculation in interval and parameter to be designed
Figure BDA0002134299120000058
And
Figure BDA0002134299120000059
meets the Hurwitz condition;
giving an update law of the weight of the neural network as
Figure BDA00021342991200000510
Wherein the content of the first and second substances,
Figure BDA00021342991200000511
is a normal number to be designed;
and step 3: the controller type (12) is designed to drive the dimensionless dynamics (4) based on the parameter adaptive law type (17) and the neural network weight updating law type (18), and the dimensionless dynamics are returned to the MEMS gyro dynamics model (1) through dimension conversion, so that gyro drive control and dynamics parameter identification are realized.
Advantageous effects
Compared with the prior art, the heterogeneous estimation-based MEMS gyroscope sliding mode control method has the beneficial effects that:
(1) aiming at the problem that the dynamic parameters are unknown in the actual engineering, the historical data information is fully mined, and the current data and the historical data are utilized to jointly construct a parameter adaptive law so as to realize parameter identification.
(2) Aiming at the uncertainty of system dynamics caused by environmental changes such as temperature, air pressure and the like, a self-adaptive neural network is designed to adjust the weight of the neural network on line, and the uncertainty effective estimation is realized.
(3) Aiming at the problem that the system is easily influenced by an external vibration environment, the sliding mode controller is designed to realize the drive control of the MEMS gyroscope and improve the robustness of the system.
Drawings
FIG. 1 is a flow chart of an embodiment of the present invention
Detailed Description
The invention will now be further described with reference to the following examples and drawings:
the invention discloses a heterogeneous estimation-based MEMS gyroscope sliding mode control method, which comprises the following specific design steps in combination with figure 1:
(a) the MEMS gyroscopic dynamics model considering the presence of quadrature errors and system uncertainty is:
Figure BDA0002134299120000061
where m is the mass of the proof mass, ΩzIn order to input the angular velocity for the gyro,
Figure BDA0002134299120000062
and x is the acceleration, velocity and displacement of the MEMS gyroscope proof mass along the driving shaft respectively,
Figure BDA0002134299120000063
and y are acceleration, velocity and displacement along the detection axis respectively,
Figure BDA0002134299120000064
and
Figure BDA0002134299120000065
as an electrostatic driving force, cxxAnd cyyAs damping coefficient, kxxAnd kyyIn order to be a stiffness factor, the stiffness factor,
Figure BDA0002134299120000066
and
Figure BDA0002134299120000067
is a nonlinear coefficient, cxyAnd cyxTo damp the coupling coefficient, kxyAnd kyxIs the stiffness coupling coefficient. And is
Figure BDA0002134299120000068
Figure BDA0002134299120000069
Wherein
Figure BDA00021342991200000610
And
Figure BDA00021342991200000611
the parameters are nominal values, and according to a certain type of vibrating silicon micromechanical gyroscope, each parameter of the gyroscope is selected to be m-5.7 multiplied by 10-9kg，q0＝10-5m，ω0＝1kHz，Ωz＝5.0rad/s，
Figure BDA0002134299120000071
Figure BDA0002134299120000072
Figure BDA0002134299120000073
Δkxx、Δkyy、Δcxx、Δcyy、
Figure BDA0002134299120000074
Δkxy、Δkyx、ΔcxyAnd Δ cyxIs an unknown uncertain parameter.
Taking the dimensionless time t as omegaot*Non-dimensionalized displacement x ═ x*/q0，y＝y*/q0Wherein ω is0As reference frequency, q0Carrying out dimensionless processing on the MEMS gyro dynamic model to obtain a reference length
Figure BDA0002134299120000075
Wherein the content of the first and second substances,
Figure BDA0002134299120000076
and x is the dimensionless acceleration, the dimensionless speed and the dimensionless displacement of the MEMS gyroscope proof mass along the driving shaft respectively,
Figure BDA0002134299120000077
and y is the dimensionless acceleration, the dimensionless velocity, and the dimensionless displacement along the detection axis, respectively.
On both sides of formula (2) simultaneously by
Figure BDA0002134299120000078
Simplify it into
Figure BDA0002134299120000079
Redefining the kinetic parameters to
Figure BDA00021342991200000710
Figure BDA00021342991200000711
The formula (3) can be represented as
Figure BDA00021342991200000712
Wherein the content of the first and second substances,
Figure BDA00021342991200000713
Figure BDA0002134299120000081
and is
Figure BDA0002134299120000082
Figure BDA0002134299120000083
Figure BDA0002134299120000084
Figure BDA0002134299120000085
Definition of
Figure BDA0002134299120000086
Figure BDA0002134299120000087
Figure BDA0002134299120000088
Figure BDA0002134299120000089
The formula (4) can be rewritten as
Figure BDA00021342991200000810
Definition of θ ═ x, y]T，F＝[f1,f2]T，ΔF＝[Δf1,Δf2]T，U＝[u1,u2]TThen formula (5) can be written as
Figure BDA00021342991200000811
Suppose that
Figure BDA00021342991200000812
Is the unknown parameter matrix to be identified,
Figure BDA00021342991200000813
if the vector is a continuous micro regression function vector, performing linear parameterization on the F to obtain
F＝WΦ (7)
Wherein the content of the first and second substances,
Figure BDA00021342991200000814
Figure BDA00021342991200000815
constructing neural networks
Figure BDA00021342991200000816
Approaches Δ F to obtain
Figure BDA00021342991200000817
Wherein the content of the first and second substances,
Figure BDA0002134299120000091
is the input vector of the neural network and,
Figure BDA0002134299120000092
is a weight matrix of the neural network, M is the number of nodes of the neural network, M is selected to be 5 multiplied by 3 multiplied by 225,
Figure BDA0002134299120000093
is a base vector, the q (q is 1,2, …, M) th element of which is defined as the following Gaussian function
Figure BDA0002134299120000094
Wherein σqIs the standard deviation of the Gaussian function, selected as σq＝1，
Figure BDA0002134299120000095
Is the center of the Gaussian function and has a value of-29.202, 29.202]×[-25.55,25.55]×[-6.2,6.2]×[-5,5]Can be selected arbitrarily.
(b) The reference trajectory given for MEMS gyroscopic dynamics (1) is
Figure BDA0002134299120000096
Wherein the content of the first and second substances,
Figure BDA0002134299120000097
and
Figure BDA0002134299120000098
reference vibration displacement signals of the proof mass along the drive axis and the proof axis, respectively.
The reference trajectory of the dimensionless kinetic equation (6) is
θd＝[xd,yd]T (11)
Wherein the content of the first and second substances,
Figure BDA0002134299120000099
and the parameters to be designed
Figure BDA00021342991200000910
Figure BDA00021342991200000911
Defining a tracking error as
e＝θ-θd (12)
The slip form surface is designed as
Figure BDA00021342991200000912
Wherein the content of the first and second substances,
Figure BDA00021342991200000913
the controller is designed as
U＝Un+Us+Ul (14)
Figure BDA00021342991200000914
Us＝-Kss (16)
Figure BDA0002134299120000101
Wherein the content of the first and second substances,
Figure BDA0002134299120000102
is an estimate of the value of W,
Figure BDA0002134299120000103
defining a prediction error as
Figure BDA0002134299120000104
Wherein the content of the first and second substances,
Figure BDA0002134299120000105
giving an adaptation law of the parameters
Figure BDA0002134299120000106
Wherein, the first term on the right side of the equation is calculated by using the data at the current moment, and the second term is calculated by using tau epsilon [ t-tau ]d,t]Historical data within the interval is calculated, and
Figure BDA0002134299120000107
giving an update law of the weight of the neural network as
Figure BDA0002134299120000108
Wherein the content of the first and second substances,
Figure BDA0002134299120000109
(d) and designing a sliding mode controller formula (14) to drive a dimensionless dynamic formula (6) based on a parameter adaptive formula (19) and an update formula (20) of the weight of the neural network, and returning to the MEMS gyro dynamic model formula (1) through dimension conversion to realize gyro drive control and dynamic parameter identification.

Claims (1)

1. A sliding mode control method of an MEMS gyroscope based on heterogeneous estimation is characterized by comprising the following steps:
step 1: the MEMS gyroscopic dynamics model considering the presence of quadrature errors and system uncertainty is:
Figure FDA0003461362500000011
where m is the mass of the proof mass, ΩzIn order to input the angular velocity for the gyro,
Figure FDA0003461362500000012
and x*Respectively the acceleration, the speed and the displacement of the MEMS gyroscope detection mass block along the driving shaft,
Figure FDA0003461362500000013
and y*Acceleration, velocity and displacement along the detection axis,
Figure FDA0003461362500000014
and
Figure FDA0003461362500000015
as an electrostatic driving force, cxxAnd cyyAs damping coefficient, kxxAnd kyyIn order to be a stiffness factor, the stiffness factor,
Figure FDA0003461362500000016
and
Figure FDA0003461362500000017
is a nonlinear coefficient, cxyAnd cyxTo damp the coupling coefficient, kxyAnd kyxIs the stiffness coupling coefficient; and is
Figure FDA0003461362500000018
Figure FDA0003461362500000019
Wherein
Figure FDA00034613625000000110
And
Figure FDA00034613625000000111
is a parameter nominal value, is selected according to a certain model of vibrating silicon micromechanical gyroscope, and is delta kxx、Δkyy、Δcxx、Δcyy、
Figure FDA00034613625000000112
Δkxy、Δkyx、ΔcxyAnd Δ cyxIs an unknown uncertain parameter;
taking the dimensionless time t as omegaot*Non-dimensionalized displacement x ═ x*/q0，y＝y*/q0Wherein ω is0As reference frequency, q0For reference length, the MEMS gyroscopic dynamics model is dimensionless and divided by the equation on both sides simultaneously
Figure FDA00034613625000000113
To obtain
Figure FDA00034613625000000114
Wherein the content of the first and second substances,
Figure FDA00034613625000000115
and x is the dimensionless acceleration, the dimensionless speed and the dimensionless displacement of the MEMS gyroscope proof mass along the driving shaft respectively,
Figure FDA00034613625000000116
and y is the dimensionless acceleration, the dimensionless speed and the dimensionless displacement along the detection axis, respectively;
redefining
Figure FDA0003461362500000021
Figure FDA0003461362500000022
Figure FDA0003461362500000023
Figure FDA0003461362500000024
Figure FDA0003461362500000025
Figure FDA0003461362500000026
Figure FDA0003461362500000027
Figure FDA0003461362500000028
Figure FDA0003461362500000029
Figure FDA00034613625000000210
The formula (2) can be represented as
Figure FDA00034613625000000211
Definition of θ ═ x, y]T，F＝[f1,f2]T，ΔF＝[Δf1,Δf2]T，U＝[u1,u2]TThen formula (3) can be written as
Figure FDA00034613625000000212
Suppose that
Figure FDA00034613625000000213
Is the unknown parameter matrix to be identified,
Figure FDA00034613625000000214
if the vector is a continuous micro regression function vector, performing linear parameterization on the F to obtain
F＝WΦ (5)
Wherein the content of the first and second substances,
Figure FDA00034613625000000215
Figure FDA00034613625000000216
constructing neural networks
Figure FDA0003461362500000031
Approaches Δ F to obtain
Figure FDA0003461362500000032
Wherein the content of the first and second substances,
Figure FDA0003461362500000033
is the input vector of the neural network and,
Figure FDA0003461362500000034
is the weight matrix of the neural network, M is the number of nodes of the neural network,
Figure FDA0003461362500000035
is a base vector, the q element of which is defined as the following Gaussian function; q ═ 1,2, …, M;
Figure FDA0003461362500000036
wherein σqIs the standard deviation of the gaussian to be designed,
Figure FDA0003461362500000037
is the center of the gaussian function to be designed;
step 2: the reference trajectory given for MEMS gyroscopic dynamics (1) is
Figure FDA0003461362500000038
Wherein the content of the first and second substances,
Figure FDA0003461362500000039
and
Figure FDA00034613625000000310
reference vibration displacement of the proof mass along the drive axis and the proof axis, respectivelyThe signal(s) is (are) transmitted,
Figure FDA00034613625000000311
and
Figure FDA00034613625000000312
reference amplitudes, ω, of drive and sense shaft vibrations, respectively1And ω2Respectively the reference angular frequencies of the drive shaft and the detection shaft vibrations,
Figure FDA00034613625000000313
and
Figure FDA00034613625000000314
the phases of the drive shaft and the detection shaft vibration respectively;
the reference trajectory of the dimensionless kinetic equation (4) is
θd＝[xd,yd]T (9)
Wherein the content of the first and second substances,
Figure FDA00034613625000000315
and the parameters to be designed
Figure FDA00034613625000000316
Figure FDA00034613625000000317
Defining a tracking error as
e＝θ-θd (10)
The slip form surface is designed as
Figure FDA00034613625000000318
Wherein the content of the first and second substances,
Figure FDA00034613625000000319
a matrix satisfying the Hurwitz condition;
the controller is designed as
U＝Un+Us+Ul (12)
Figure FDA0003461362500000041
Us＝-Kss (14)
Figure FDA0003461362500000042
Wherein the parameter to be designed
Figure FDA0003461362500000043
The Hurwitz condition is met,
Figure FDA0003461362500000044
is an estimate of W;
defining a prediction error as
Figure FDA0003461362500000045
Wherein the content of the first and second substances,
Figure FDA0003461362500000046
τdis a normal number to be designed;
giving an adaptation law of the parameters
Figure FDA0003461362500000047
Wherein, the first term on the right side of the equation is calculated by using the data at the current moment, and the second term is calculated by using tau epsilon [ t-tau ]d,t]Historical data calculation in interval and parameter to be designed
Figure FDA0003461362500000048
And
Figure FDA0003461362500000049
meets the Hurwitz condition;
giving an update law of the weight of the neural network as
Figure FDA00034613625000000410
Wherein the content of the first and second substances,
Figure FDA00034613625000000411
is a normal number to be designed;
and step 3: the controller type (12) is designed to drive the dimensionless dynamics (4) based on the parameter adaptive law type (17) and the neural network weight updating law type (18), and the dimensionless dynamics are returned to the MEMS gyro dynamics model (1) through dimension conversion, so that gyro drive control and dynamics parameter identification are realized.
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